Fractal and Fractional, Volume 6, Issue 8

In this paper, we develop a numerical scheme that conserves the discrete energy for solving the Klein-Gordon equation with cubic nonlinearity. We prove theoretically that our scheme conserves not just discrete energy, but also other energy-like discr...

Porous alumina was prepared by the sacrificial template approach using 30 vol.%, 50 vol.%, and 70 vol.% of carbon fibers and graphite as pore formers. In order to determine the pore size distribution, porosity, most probable pore size, and median por...

In this paper, we investigate a duopolistic market with heterogeneous firms under the assumptions of an isoelastic demand and quadratic costs. We obtain the sufficient and necessary condition of the local stability of the Cournot–Nash equilibri...

Alzheimer’s disease (AD) is an age-related degenerative disorder of the cerebral neuro-glial-vascular units. Not only are post-menopausal females, especially those who carry the APOE4 gene, at a higher risk of AD than males, but also AD in fema...

SEM microfractographies of Zircaloy-4 are studied by fractal analysis and the time-series method. We first develop a computer application that associates the fractal dimension and lacunarity to each SEM micrograph picture, and produce a nonlinear ana...

Fractional-order systems have proved to be accurate in describing the spread of the COVID-19 pandemic by virtue of their capability to include the memory effects into the system dynamics. This manuscript presents a novel fractional discrete-time COVI...

The idea of best proximity points of the fuzzy mappings in fuzzy metric space was intorduced by Vetro and Salimi. We introduce a new type of proximal contractive condition that ensures the existence of best proximity points of fuzzy mappings in the f...

Let $B^H=\{B_t^H,t\ge 0\}$ be a fractional Brownian motion with Hurst index $\frac{1}{2}\le H<1$. In this paper, we consider the linear self-attracting diffusion: $d{X}_t^H=d{B}_t^H+\sigma X_t^{H}dt-\theta \left({\int }_0^t\left(X_s^H-X_u^H\right)ds\right)dt$$+\nu dt$ with $X_0^H=0$, where $\theta >0$ and...

Fractional factorial split-plot designs are widely used when it is impractical to perform fractional factorial experiments in a completely random order. When there are too many subplots per whole plot, or too few whole plots, fractional factorial spl...

This study develops a numerical strategy for finding the approximate solution of the nonlinear foam drainage (NFD) equation with a time-fractional derivative. In this paper, we formulate the idea of the Laplace homotopy perturbation transform method...

This paper investigates the local stabilization problem of delayed fractional-order neural networks (FNNs) under the influence of actuator saturation. First, the sector condition and dead-zone nonlinear function are specially introduced to characteri...

In this paper, we study a class of nonlinear space-time fractional stochastic kinetic equations in ${\mathbb{R}}^d$ with Gaussian noise which is white in time and homogeneous in space. This type of equation constitutes an extension of the nonlinear stochastic heat...

The purpose of this study is to offer a systematic, unified approach to the Mellin-Barnes integrals and associated special functions as Fox H, Aleph ℵ, and Saxena I function, encompassing the fundamental features and important conclusions und...

The main goal of this work is to optimize the chaotic behavior of a three-dimensional chaotic-spherical-attractor-generating fractional-order system and compare the results with its novel hyperchaotic counterpart. The fractional-order chaotic system...

The technological development in wind energy conversion systems (WECSs) places emphasis on the injection of wind power into the grid in a smoother and robust way. Sliding mode control (SMC) has proven to be a popular solution for the grid-connected W...

This article studies a biological population model in the context of a fractional Caputo-Fabrizio operator using double Laplace transform combined with the Adomian method. The conditions for the existence and uniqueness of solution of the problem und...

The fractional mobile/immobile solute transport model has applications in a wide range of phenomena such as ocean acoustic propagation and heat diffusion. The local radial basis functions (RBFs) method have been applied to many physical and engineeri...

We construct soliton solutions of the complex time fractional Schrodinger model (tFSM), as well as the space–time fractional differential model (stFDM), leading wave spread through electrical transmission lines model (ETLM) in low pass with the...

In this paper, an implicit difference scheme is proposed and analyzed for a class of nonlinear fourth-order equations with the multi-term Riemann–Liouvile (R–L) fractional integral kernels. For the nonlinear convection term, we handle imp...

This paper deals with the asymptotic synchronization of fractional-order complex dynamical networks with different structures and parameter uncertainties (FCDNDP). Firstly, the FCDNDP model is proposed by the Riemann–Liouville (R-L) fractional...

Among the numerous applications of the theory of fractional calculus in almost all applied sciences, applications in numerical analysis and various fields of physics and engineering stand out [...]

This paper initiates a study on the existence and approximate controllability for a type of non-instantaneous impulsive stochastic evolution equation (ISEE) excited by fractional Brownian motion (fBm) with Hurst index $0<H<1/2$. First, to overcom...

We present a finite difference/spectral method for the two-dimensional generalized time fractional cable equation by combining the second-order backward difference method in time and the Galerkin spectral method in space with Legendre polynomials. Th...

The time-fractional Cattaneo equation is an equation where the fractional order $\alpha \in (1,2)$ has the capacity to model the anomalous dynamics of physical diffusion processes. In this paper, we consider an efficient scheme for solving such an eq...

In our present investigation, a subclass of starlike function ${\mathcal{S}}_{n-1,\mathcal{L}}^{*}$ connected with a domain bounded by an epicycloid with $n-1$ cusps was considered. The main work is to investigate some coefficient inequalities, and second and third Hankel determina...

Motivated by the recent interest in generalized fractional order operators and their applications, we consider some classes of integro-differential initial value problems based on derivatives of the Riemann–Liouville and Caputo form, but with n...

A new auxiliary result pertaining to twice (${\mathrm{q}}_1,{\mathrm{q}}_2$)-differentiable functions is derived. Using this new auxiliary result, some new versions of Hermite–Hadamard’s inequality involving the class of generalized $\mathfrak{m}$-convex functions are obtained. Finally, t...

We study a class of nonlinear fractional differential equations with multiple delays, which is represented by the Voigt creep fractional model of viscoelasticity. We discuss two Voigt models, the first being linear and the second being nonlinear. The...

This paper mainly considers the parameter estimation problem for several types of differential equations controlled by linear operators, which may be partial differential, integro-differential and fractional order operators. Under the idea of data-dr...

This paper proposes an algorithm and hardware realization of generalized chaotic systems using fractional calculus and rotation algorithms. Enhanced chaotic properties, flexibility, and controllability are achieved using fractional orders, a multi-sc...

In this paper, by considering the notions of the invex set, Fréchet differentiability, invexity and pseudoinvexity for the involved functionals of curvilinear integral type, we establish some relations between the solutions of a class of weak...

Langmuir waves propagate in fractal complex plasma with fractal characteristics, which may cause some plasma particles to be trapped or causes wave turbulences. This phenomenon appears in the form of fractional order equations. Using an effective uni...

This paper addresses the problems of the stability of a nabla discrete distributed-order dynamical system (NDDS). Firstly, based on a proposed generalized definition of discrete integral, some related definitions of nabla discrete distributed-order c...

In this paper, circuit implementation and anti-synchronization are studied in coupled nonidentical fractional-order chaotic systems where a fractance module is introduced to approximate the fractional derivative. Based on the open-plus-closed-loop co...

The authors of this paper systematically studied the mechanical properties and durability of concrete prepared with copper slag instead of natural aggregates. An analysis index was used to assess compressive strength, and a statistical method was use...

In this paper, we implement computational methods, namely the local fractional natural homotopy analysis method (LFNHAM) and local fractional natural decomposition method (LFNDM), to examine the solution for the local fractional Lighthill–Whith...

The celebrated Korteweg–de Vries and Kadomtsev–Petviashvili (KP) equations are prototypical examples of integrable evolution equations in one and two spatial dimensions, respectively. The question of constructing integrable evolution equa...

This manuscript mainly discusses the approximate controllability for certain fractional delay evolution equations in Banach spaces. We introduce a suitable complete space to deal with the disturbance due to the time delay. Compared with many related...

A compact triple-band operation ultra-wideband (UWB) antenna with dual-notch band characteristics is presented in this paper. By inserting three metamaterial (MTM) square split-ring resonators (MTM-SSRRs) and a triangular slot on the radiating patch,...

Cyclic loading always results in great damage to the pore structure and fractal characteristics of soft soil. Scanning electron microscope (SEM) can help collect data to describe the microstructure of soft soil. This paper conducted a series of SEM t...

The aim of this research is to identify an efficient model to describe the fluctuations around the trend of the soil temperatures monitored in the volcanic caldera of the Campi Flegrei area in Naples (Italy). This study focuses on the data concerning...

In mathematics, physics, and engineering, orthogonal polynomials and special functions play a vital role in the development of numerical and analytical approaches. This field of study has received a lot of attention in recent decades, and it is gaini...

Partial differential equations are known to be increasingly important in today’s research, and their solutions are paramount for tackling numerous real-life applications. This article extended the analytical scheme of the homotopy analysis meth...

This paper proposes a new fractional Poisson process through a recursive fractional differential governing equation. Unlike the homogeneous Poison process, the Caputo derivative on the probability distribution of k jumps with respect to time is linke...

An exponential-type function was discovered to transform known difference formulas by involving a shifted parameter $\theta$ to approximate fractional calculus operators. In contrast to the known $\theta$ methods obtained by polynomial-type transformat...

The sampled-data stabilization of a fractional continuous linear system under arbitrary sampling periods was first investigated in this paper wherein novel co-designed sampled-data controllers were constructed based on the compensation of scaling gai...

The theory of convex and nonconvex mapping has a lot of applications in the field of applied mathematics and engineering. The Riemann integrals are the most significant operator of interval theory, which permits the generalization of the classical th...

The stochastic resonance (SR) of a star-coupled harmonic oscillator subject to multiplicative fluctuation and periodic force in viscous media is studied. The multiplicative noise is modeled as a dichotomous noise and the memory of viscous media is ch...

The fuzzy differential subordination concept was introduced in 2011, generalizing the concept of differential subordination following a recent trend of adapting fuzzy sets theory to other already-established theories. A prolific tool in obtaining new...

In this paper, the Fischer–Burmeister active-set trust-region (FBACTR) algorithm is introduced to solve the nonlinear bilevel programming problems. In FBACTR algorithm, a Karush–Kuhn–Tucker (KKT) condition is used with the Fischer&n...